Counting Models Using Connected Components

Recent work by Birnbaum & Lozinskii [1999] demonstrated that a clever yet simple extension of the well-known DavisPutnam procedure for solving instances of propositional satisfiability yields an efficient scheme for counting the number of satisfying assignments (models). We present a new extension, based on recursively identifying connected constraint-graph components, that substantially improves counting performance on random 3-SAT instances as well as benchmark instances from the SATLIB and Beijing suites. In addition, from a structure-based perspective of worst-case complexity, while polynomial time satisfiability checking is known to require only a backtrack search algorithm enhanced with nogood learning, we show that polynomial time counting using backtrack search requires an additional enhancement: good learning.

[1]  Eliezer L. Lozinskii.  Counting Propositional Models , 1992, Inf. Process. Lett..

[2]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Real-World SAT Instances , 1997, AAAI/IAAI.

[3]  John Beidler,et al.  Data Structures and Algorithms , 1996, Wiley Encyclopedia of Computer Science and Engineering.

[4]  Patrick Prosser,et al.  HYBRID ALGORITHMS FOR THE CONSTRAINT SATISFACTION PROBLEM , 1993, Comput. Intell..

[5]  Michael J. Quinn,et al.  Taking Advantage of Stable Sets of Variables in Constraint Satisfaction Problems , 1985, IJCAI.

[6]  Eliezer L. Lozinskii,et al.  The Good Old Davis-Putnam Procedure Helps Counting Models , 2011, J. Artif. Intell. Res..

[7]  Rina Dechter,et al.  Network-based heuristics for constraint satisfaction problems , 1988 .

[8]  James M. Crawford,et al.  Experimental Results on the Crossover Point in Random 3-SAT , 1996, Artif. Intell..

[9]  Daniel I. Miranker,et al.  ce-Bounded Learning Algorith Constraint Satisfaction Problem , 1999 .

[10]  Daniel P. Miranker,et al.  On the Space-Time Trade-off in Solving Constraint Satisfaction Problems , 1995, IJCAI.

[11]  J. Freeman.  Improvements to propositional satisfiability search algorithms , 1995 .

[12]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[13]  Rina Dechter,et al.  Dead-End Driven Learning , 1994, AAAI.

[14]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[15]  Daniel P. Miranker,et al.  An Optimal Backtrack Algorithm for Tree-Structured Constraint Satisfaction problems , 1994, Artif. Intell..

[16]  Daniel P. Miranker,et al.  A Complexity Analysis of Space-Bounded Learning Algorithms for the Constraint Satisfaction Problem , 1996, AAAI/IAAI, Vol. 1.

[17]  Tad Hogg,et al.  Refining the Phase Transition in Combinatorial Search , 1996, Artif. Intell..

[18]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[19]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .